I'd say no. As a rule of thumb, you should use as much money on lenses as on the camera itself, and using that much money on equipment with as little experience as you have doesn't sound like a good move. I'd rather focus more on other elements of filmmaking at the beginning, and if you want a new camera, rather look at something like blackmagic pocket cinema camera or blackmagic cinema camera. It's not as big of an investment, and you'll still be able to tell great stories.
That's what I though. I'll mostly make non-profitable films the next year, so renting lenses will be problematic. I'll go for the EF-mount then. Thanks for the answer!
When beginning I'd recommend just using whatever you can get your hands on. A DSLR camera is a good place to begin, if you can get your hands on one. If not I'd just use a smartphone or something along those lines. I'd also try to get my hands on a tripod, but it's not essential.
As for editing I usually use Premiere Pro. This can however be expensive, so you could check out DaVinci resolve Lite, which is a newly released free version of Davinci Resolve. The program is quite easy to get into, plus the color correction is quite good.
I'd also recommend getting some extra light, it's good to get into that as soon as possible. I started out with some work lights, it's not perfect, but you shouldn't have much problem finding some, while professional lights can be really expensive.
As for what to shoot, I'd say whatever inspires you. Just remember that pre-production sets the standard for the rest of the film. Work hard on this. That includes a good screenplay, where I'd recommend checking out the program Adobe Story, which is free, and a solid screenplay.
In the production, I'd say you need to be at least a total of three people. This is how I made my first productions, and fewer than that made it almost impossible. With three people you'll be able to have one camera operator, and two actors. This is of course a problem if you need someone to hold a microphone or something like that.
Remember to take your time. Making films, even short films is a long, long process. Start out making 1-3 minutes of edited film, and you'll learn tons of new stuff for each new project.
I always try to do as little as possible in the post-production, but with some planning you could get a quite good result by stabilizing the clip in the editing with programs like Adobe After Effects or Premiere.